Assessing Algebra Concepts in Adults

Instructor: Matt Gromlich

Matt has taught at the K-12 level and beyond for the last five years. He is currently getting his Ph.D. in Mathematics Education.

This lesson plan provides strategies for assessing adult basic education (ABE) students in algebra. It discusses basic andragogical approaches and frameworks and give examples of algebra assessments.

Pedagogy vs. Andragogy

The study and practice of childhood education is often referred to as pedagogy. A lesser-known term is andragogy, a word used in adult education, because it translates to ''leader of man.''

Malcolm Knowles is known as the father of andragogy because he was one of the first to study it as a methodological framework. In the 1980s, Knowles identified five key factors that affect adult students' motivation that are not present in child learners:

  1. Self-concept
  2. Adult learner experience
  3. Readiness to learn
  4. Orientation to learning
  5. Motivation to learn

By the time adult learners decide to come back to school, they have already developed a self-concept. That's why it's necessary for adult educators to incorporate self-concept into their lesson plans and andragogical approaches to teaching.

Using Scaffolding to Assess Students

In algebra, as in other mathematical disciplines, problems tend to increase in difficulty as a chapter or unit progresses. Scaffolding is an approach teachers use to slowly increase the difficultly level of problems. Teachers purposefully and thoughtfully choose problems that initially teach a skill. Additional problems add another layer or level of complexity that allows students to build upon previous knowledge and feel successful in the process.

An example of scaffolding in algebra is teaching problem-solving techniques, beginning with one-step addition equations, like x + 5 = 9. Here, you'd explain how to arrive at the answer algebraically by subtracting ''5'' from both sides of the equation: x = 4. You'd then move on to one-step subtraction, multiplication, and division equations. Once students are comfortable with one-step equations with positive and negative numbers, you'd then use scaffolding to teach two-step equations.

Whiteboard Technique

To assess learning using the scaffolding technique, give each student a small whiteboard and assign them a problem. Students must show all of their work and raise their boards when they're finished. This allows you to easily assess who has conceptual understanding and who has procedural fluency. For example, some students may understand the concept without having the numeracy skills to solve the problem accurately.

Using Dialogue to Assess Students

When modeling problems for students, the ''I-do, we-do, you-do'' method can be extremely effective. In this method, teachers explain how to approach and solve problems, after which students work through similar problems as a class and individually.

The dialogue that occurs in the ''I-do, we-do, you-do'' method allows you to formatively assess student learning by modeling appropriate mathematical dialogue for your students. Then, when students are working individually or in small groups, ask them some questions. If students can use the same terminology and vocabulary included in the model, then you know they're beginning to digest and understand the information.

Using Peer Assessment to Assess Students

Peer assessment is an extremely valuable tool used in pedagogical and andragogical frameworks. Using the think-pair-share method, students answer a question individually and then compare their answers to their partners' answers. This provides immediate feedback for both students and teachers. This formative assessment method is beneficial, because teachers can listen to conversations and make sure that students understand the material.

An extension of this method is the ''think-pair-square method.'' Here, each pair then pairs with another pair so that four students have the chance to compare answers and thought processes.

Using Feedback to Assess Students

A positive, inclusive classroom culture is important in adult education. As a teacher, it's your responsibility to let students know that you understand how difficult algebra can be - especially if they haven't used this type of mathematics in the last few years.

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